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Simulating Stochastic Differential Equations with Conserved Quantities by Improved Explicit Stochastic Runge–Kutta Methods

Author

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  • Zhenyu Wang

    (Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, China)

  • Qiang Ma

    (Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, China)

  • Xiaohua Ding

    (Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, China)

Abstract

Explicit numerical methods have a great advantage in computational cost, but they usually fail to preserve the conserved quantity of original stochastic differential equations (SDEs). In order to overcome this problem, two improved versions of explicit stochastic Runge–Kutta methods are given such that the improved methods can preserve conserved quantity of the original SDEs in Stratonovich sense. In addition, in order to deal with SDEs with multiple conserved quantities, a strategy is represented so that the improved methods can preserve multiple conserved quantities. The mean-square convergence and ability to preserve conserved quantity of the proposed methods are proved. Numerical experiments are implemented to support the theoretical results.

Suggested Citation

  • Zhenyu Wang & Qiang Ma & Xiaohua Ding, 2020. "Simulating Stochastic Differential Equations with Conserved Quantities by Improved Explicit Stochastic Runge–Kutta Methods," Mathematics, MDPI, vol. 8(12), pages 1-15, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2195-:d:459447
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    References listed on IDEAS

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